Decorrelation-Based Feature Discovery: GI-Whole

1 Effect of UPSTM-Based Decorrelation on Feature Discovery

1.0.1 Loading the libraries

library("FRESA.CAD")
library(readxl)
library(igraph)
library(umap)
library(tsne)
library(entropy)

op <- par(no.readonly = TRUE)
pander::panderOptions('digits', 3)
pander::panderOptions('table.split.table', 400)
pander::panderOptions('keep.trailing.zeros',TRUE)

1.1 Material and Methods

1.2 The Data

dataGI <- as.data.frame(read_excel("~/GitHub/LatentBiomarkers/Data/GI/data.xlsx", sheet = "Sheet1"))
dataGI$ID <- NULL

table(dataGI$V2)
#> 
#>  1  2 
#> 76 76
dataSet1 <- subset(dataGI,V2==1)
class <- dataSet1$V1
dataSet1$V1 <- NULL
dataSet1$V2 <- NULL
colnames(dataSet1) <- paste(colnames(dataSet1),"WL",sep="_")
dataSet2 <- subset(dataGI,V2==2)
dataSet2$V1 <- NULL
dataSet2$V2 <- NULL
colnames(dataSet2) <- paste(colnames(dataSet2),"NBI",sep="_")
dataGI <- cbind(dataSet1,dataSet2)
dataGI$class <- 1*(class > 1)
table(dataGI$class)
#> 
#>  0  1 
#> 21 55

1.2.0.1 Standarize the names for the reporting

studyName <- "GI"
dataframe <- dataGI
outcome <- "class"

TopVariables <- 10

thro <- 0.80
cexheat = 0.15

1.3 Generaring the report

1.3.1 Libraries

Some libraries

library(psych)
library(whitening)
library("vioplot")
library("rpart")

1.3.2 Data specs

pander::pander(c(rows=nrow(dataframe),col=ncol(dataframe)-1))

rows	col
76	1396

pander::pander(table(dataframe[,outcome]))

0	1
21	55

varlist <- colnames(dataframe)
varlist <- varlist[varlist != outcome]

largeSet <- length(varlist) > 1500 

1.3.3 Scaling the data

Scaling and removing near zero variance columns and highly co-linear(r>0.99999) columns

  ### Some global cleaning
  sdiszero <- apply(dataframe,2,sd) > 1.0e-16
  dataframe <- dataframe[,sdiszero]

  varlist <- colnames(dataframe)[colnames(dataframe) != outcome]
  tokeep <- c(as.character(correlated_Remove(dataframe,varlist,thr=0.99999)),outcome)
  dataframe <- dataframe[,tokeep]

  varlist <- colnames(dataframe)
  varlist <- varlist[varlist != outcome]
  
  iscontinous <- sapply(apply(dataframe,2,unique),length) >= 5 ## Only variables with enough samples



dataframeScaled <- FRESAScale(dataframe,method="OrderLogit")$scaledData

1.4 The heatmap of the data

numsub <- nrow(dataframe)
if (numsub > 1000) numsub <- 1000


if (!largeSet)
{

  hm <- heatMaps(data=dataframeScaled[1:numsub,],
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 xlab="Feature",
                 ylab="Sample",
                 srtCol=45,
                 srtRow=45,
                 cexCol=cexheat,
                 cexRow=cexheat
                 )
  par(op)
}

1.4.0.1 Correlation Matrix of the Data

The heat map of the data

if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  #cormat <- Rfast::cora(as.matrix(dataframe[,varlist]),large=TRUE)
  cormat <- cor(dataframe[,varlist],method="pearson")
  cormat[is.na(cormat)] <- 0
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Original Correlation",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="|Pearson Correlation|",
                    xlab="Feature", ylab="Feature")
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 0.9999797

1.5 The decorrelation

DEdataframe <- IDeA(dataframe,verbose=TRUE,thr=thro)
#> 
#>  Included: 725 , Uni p: 0.01309165 , Uncorrelated Base: 29 , Outcome-Driven Size: 0 , Base Size: 29 
#> 
#> 
 1 <R=1.000,r=0.975,N=  185>, Top: 31( 29 )[ 1 : 31 Fa= 30 : 0.975 ]( 30 , 78 , 0 ),<|>Tot Used: 108 , Added: 78 , Zero Std: 0 , Max Cor: 1.000
#> 
 2 <R=1.000,r=0.975,N=  185>, Top: 8( 26 )[ 1 : 8 Fa= 38 : 0.975 ]( 8 , 51 , 30 ),<|>Tot Used: 153 , Added: 51 , Zero Std: 0 , Max Cor: 1.000
#> 
 3 <R=1.000,r=0.975,N=  185>, Top: 7( 15 )[ 1 : 7 Fa= 44 : 0.975 ]( 7 , 30 , 38 ),<|>Tot Used: 178 , Added: 30 , Zero Std: 0 , Max Cor: 0.999
#> 
 4 <R=0.999,r=0.975,N=  185>, Top: 5( 6 )[ 1 : 5 Fa= 48 : 0.975 ]( 4 , 24 , 44 ),<|>Tot Used: 181 , Added: 24 , Zero Std: 0 , Max Cor: 0.975
#> 
 5 <R=0.975,r=0.962,N=  185>, Top: 53( 1 )[ 1 : 53 Fa= 80 : 0.962 ]( 51 , 59 , 48 ),<|>Tot Used: 247 , Added: 59 , Zero Std: 0 , Max Cor: 0.974
#> 
 6 <R=0.974,r=0.962,N=  185>, Top: 4( 1 )[ 1 : 4 Fa= 83 : 0.962 ]( 4 , 4 , 80 ),<|>Tot Used: 251 , Added: 4 , Zero Std: 0 , Max Cor: 0.962
#> 
 7 <R=0.962,r=0.931,N=  222>, Top: 75[ 3 ]( 1 )=[ 2 : 75 Fa= 127 : 0.942 ]( 72 , 105 , 83 ),<|>Tot Used: 368 , Added: 105 , Zero Std: 0 , Max Cor: 0.994
#> 
 8 <R=0.994,r=0.947,N=  222>, Top: 9( 1 )[ 1 : 9 Fa= 135 : 0.947 ]( 9 , 9 , 127 ),<|>Tot Used: 383 , Added: 9 , Zero Std: 0 , Max Cor: 0.941
#> 
 9 <R=0.941,r=0.871,N=  302>, Top: 93( 1 )=[ 2 : 93 Fa= 182 : 0.911 ]( 87 , 139 , 135 ),<|>Tot Used: 523 , Added: 139 , Zero Std: 0 , Max Cor: 0.960
#> 
 10 <R=0.960,r=0.880,N=  302>, Top: 20( 1 )[ 1 : 20 Fa= 191 : 0.880 ]( 18 , 26 , 182 ),<|>Tot Used: 545 , Added: 26 , Zero Std: 0 , Max Cor: 0.915
#> 
 11 <R=0.915,r=0.807,N=  245>, Top: 73( 5 )[ 1 : 73 Fa= 219 : 0.807 ]( 71 , 121 , 191 ),<|>Tot Used: 593 , Added: 121 , Zero Std: 0 , Max Cor: 0.926
#> 
 12 <R=0.926,r=0.813,N=  245>, Top: 17( 3 )[ 1 : 17 Fa= 226 : 0.813 ]( 16 , 20 , 219 ),<|>Tot Used: 610 , Added: 20 , Zero Std: 0 , Max Cor: 0.851
#> 
 13 <R=0.851,r=0.800,N=   49>, Top: 23( 1 )[ 1 : 23 Fa= 234 : 0.800 ]( 23 , 26 , 226 ),<|>Tot Used: 626 , Added: 26 , Zero Std: 0 , Max Cor: 0.799
#> 
 14 <R=0.799,r=0.800,N=   49>
#> 
 [ 14 ], 0.7986822 Decor Dimension: 626 Nused: 626 . Cor to Base: 244 , ABase: 17 , Outcome Base: 0 
#> 
varlistc <- colnames(DEdataframe)[colnames(DEdataframe) != outcome]

pander::pander(sum(apply(dataframe[,varlist],2,var)))

7.73e+08

pander::pander(sum(apply(DEdataframe[,varlistc],2,var)))

1.8e+08

pander::pander(entropy(discretize(unlist(dataframe[,varlist]), 256)))

0.306

pander::pander(entropy(discretize(unlist(DEdataframe[,varlistc]), 256)))

0.218

1.5.1 The decorrelation matrix

if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  
  UPSTM <- attr(DEdataframe,"UPSTM")
  
  gplots::heatmap.2(1.0*(abs(UPSTM)>0),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Decorrelation matrix",
                    cexRow = cexheat,
                    cexCol = cexheat,
                   srtCol=45,
                   srtRow=45,
                    key.title=NA,
                    key.xlab="|Beta|>0",
                    xlab="Output Feature", ylab="Input Feature")
  
  par(op)
}

1.6 The heatmap of the decorrelated data

if (!largeSet)
{

  hm <- heatMaps(data=DEdataframe[1:numsub,],
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 cexRow = cexheat,
                 cexCol = cexheat,
                 srtCol=45,
                 srtRow=45,
                 xlab="Feature",
                 ylab="Sample")
  par(op)
}

1.7 The correlation matrix after decorrelation

if (!largeSet)
{

  cormat <- cor(DEdataframe[,varlistc],method="pearson")
  cormat[is.na(cormat)] <- 0
  
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Correlation after IDeA",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="|Pearson Correlation|",
                    xlab="Feature", ylab="Feature")
  
  par(op)
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 0.9419448

1.8 U-MAP Visualization of features

1.8.1 The UMAP based on LASSO on Raw Data

if (nrow(dataframe) < 1000)
{
  classes <- unique(dataframe[1:numsub,outcome])
  raincolors <- rainbow(length(classes))
  names(raincolors) <- classes
  datasetframe.umap = umap(scale(dataframe[1:numsub,varlist]),n_components=2)
  plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: Original",t='n')
  text(datasetframe.umap$layout,labels=dataframe[1:numsub,outcome],col=raincolors[dataframe[1:numsub,outcome]+1])
}

1.8.2 The decorralted UMAP

if (nrow(dataframe) < 1000)
{

  datasetframe.umap = umap(scale(DEdataframe[1:numsub,varlistc]),n_components=2)
  plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: After IDeA",t='n')
  text(datasetframe.umap$layout,labels=DEdataframe[1:numsub,outcome],col=raincolors[DEdataframe[1:numsub,outcome]+1])
}

1.9 Univariate Analysis

1.9.1 Univariate

univarRAW <- uniRankVar(varlist,
               paste(outcome,"~1"),
               outcome,
               dataframe,
               rankingTest="AUC")

100 : V102_WL 200 : V288_WL 300 : V535_WL 400 : V635_WL 500 : V37_NBI
600 : V137_NBI 700 : V470_NBI

univarDe <- uniRankVar(varlistc,
               paste(outcome,"~1"),
               outcome,
               DEdataframe,
               rankingTest="AUC",
               )

100 : La_V102_WL 200 : La_V288_WL 300 : La_V535_WL 400 : La_V635_WL 500 : La_V37_NBI
600 : La_V137_NBI 700 : La_V470_NBI

1.9.2 Final Table

univariate_columns <- c("caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC")

##top variables
topvar <- c(1:length(varlist)) <= TopVariables
tableRaw <- univarRAW$orderframe[topvar,univariate_columns]
pander::pander(tableRaw)

	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC
V172_WL	3.55e+03	1.78e+03	1046.667	537.2409	0.718095	0.933
V220_NBI	2.01e+02	1.20e+02	51.524	27.8220	0.747592	0.929
V220_WL	1.96e+02	1.07e+02	52.381	42.7370	0.097268	0.927
V477_NBI	6.18e-02	2.98e-02	0.149	0.1717	0.000358	0.925
V169_NBI	1.26e+03	8.24e+02	346.619	198.5476	0.350000	0.920
V196_NBI	4.52e+02	2.51e+02	134.238	66.3226	0.410564	0.920
V182_NBI	3.44e+02	2.17e+02	95.190	48.8412	0.793090	0.915
V470_NBI	3.79e-01	1.34e-01	0.188	0.0682	0.948083	0.913
V182_WL	3.17e+02	1.69e+02	96.476	87.3691	0.142781	0.912
V474_NBI	3.40e+00	3.13e-01	2.680	0.5481	0.222068	0.912

topLAvar <- univarDe$orderframe$Name[str_detect(univarDe$orderframe$Name,"La_")]
topLAvar <- unique(c(univarDe$orderframe$Name[topvar],topLAvar[1:as.integer(TopVariables/2)]))
finalTable <- univarDe$orderframe[topLAvar,univariate_columns]


pander::pander(finalTable)

	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC
V474_NBI	3.40e+00	3.13e-01	2.68e+00	5.48e-01	0.2221	0.912
V169_WL	1.20e+03	6.66e+02	4.03e+02	4.20e+02	0.0543	0.897
V474_WL	3.19e+00	4.57e-01	2.36e+00	5.29e-01	0.9972	0.882
V4_WL	1.67e+03	9.90e+02	6.00e+02	4.77e+02	0.0868	0.874
La_V69_WL	1.03e-03	1.66e-03	-1.02e-03	1.56e-03	0.3074	0.872
V473_NBI	1.22e-01	4.19e-02	2.12e-01	1.67e-01	0.0188	0.865
V485_WL	3.14e+00	4.63e-01	2.44e+00	4.51e-01	0.5556	0.853
V473_WL	1.57e-01	5.21e-02	2.82e-01	1.38e-01	0.3081	0.850
V198_NBI	3.83e+02	2.17e+02	1.54e+02	9.18e+01	0.3333	0.844
La_V200_NBI	-1.08e+03	2.09e+03	1.03e+03	2.22e+03	0.0393	0.835
La_V91_NBI	6.01e-03	4.07e-03	1.88e-03	2.59e-03	0.9531	0.825
La_V478_WL	9.13e-01	2.30e-02	9.48e-01	3.09e-02	0.9838	0.824
La_V296_NBI	-3.21e+02	1.47e+03	3.76e+02	9.94e+02	0.0346	0.810

dc <- getLatentCoefficients(DEdataframe)
fscores <- attr(DEdataframe,"fscore")


pander::pander(c(mean=mean(sapply(dc,length)),total=length(dc),fraction=length(dc)/(ncol(dataframe)-1)))

mean	total	fraction
2.35	546	0.748

theCharformulas <- attr(dc,"LatentCharFormulas")


finalTable <- rbind(finalTable,tableRaw[topvar[!(topvar %in% topLAvar)],univariate_columns])


orgnamez <- rownames(finalTable)
orgnamez <- str_remove_all(orgnamez,"La_")
finalTable$RAWAUC <- univarRAW$orderframe[orgnamez,"ROCAUC"]
finalTable$DecorFormula <- theCharformulas[rownames(finalTable)]
finalTable$fscores <- fscores[rownames(finalTable)]

Final_Columns <- c("DecorFormula","caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC","RAWAUC","fscores")

finalTable <- finalTable[order(-finalTable$ROCAUC),]
pander::pander(finalTable[,Final_Columns])

	DecorFormula	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC	RAWAUC	fscores
V172_WL	NA	3.55e+03	1.78e+03	1.05e+03	5.37e+02	0.718095	0.933	0.933	NA
V220_NBI	NA	2.01e+02	1.20e+02	5.15e+01	2.78e+01	0.747592	0.929	0.929	NA
V220_WL	NA	1.96e+02	1.07e+02	5.24e+01	4.27e+01	0.097268	0.927	0.927	NA
V477_NBI	NA	6.18e-02	2.98e-02	1.49e-01	1.72e-01	0.000358	0.925	0.925	NA
V169_NBI	NA	1.26e+03	8.24e+02	3.47e+02	1.99e+02	0.350000	0.920	0.920	NA
V196_NBI	NA	4.52e+02	2.51e+02	1.34e+02	6.63e+01	0.410564	0.920	0.920	NA
V182_NBI	NA	3.44e+02	2.17e+02	9.52e+01	4.88e+01	0.793090	0.915	0.915	NA
V470_NBI	NA	3.79e-01	1.34e-01	1.88e-01	6.82e-02	0.948083	0.913	0.913	NA
V474_NBI	NA	3.40e+00	3.13e-01	2.68e+00	5.48e-01	0.222068	0.912	0.912	NA
V182_WL	NA	3.17e+02	1.69e+02	9.65e+01	8.74e+01	0.142781	0.912	0.912	NA
V474_NBI1	NA	3.40e+00	3.13e-01	2.68e+00	5.48e-01	0.222068	0.912	NA	NA
V169_WL	NA	1.20e+03	6.66e+02	4.03e+02	4.20e+02	0.054330	0.897	0.897	9
V474_WL	NA	3.19e+00	4.57e-01	2.36e+00	5.29e-01	0.997159	0.882	0.882	NA
V4_WL	NA	1.67e+03	9.90e+02	6.00e+02	4.77e+02	0.086777	0.874	0.874	4
La_V69_WL	- (1.863)V47_WL + V69_WL	1.03e-03	1.66e-03	-1.02e-03	1.56e-03	0.307376	0.872	0.617	-1
V473_NBI	NA	1.22e-01	4.19e-02	2.12e-01	1.67e-01	0.018789	0.865	0.865	2
V485_WL	NA	3.14e+00	4.63e-01	2.44e+00	4.51e-01	0.555561	0.853	0.853	1
V473_WL	NA	1.57e-01	5.21e-02	2.82e-01	1.38e-01	0.308090	0.850	0.850	1
V198_NBI	NA	3.83e+02	2.17e+02	1.54e+02	9.18e+01	0.333253	0.844	0.844	13
La_V200_NBI	- (0.862)V184_NBI + V200_NBI	-1.08e+03	2.09e+03	1.03e+03	2.22e+03	0.039308	0.835	0.763	-1
La_V91_NBI	- (2.866)V47_NBI + V91_NBI	6.01e-03	4.07e-03	1.88e-03	2.59e-03	0.953148	0.825	0.578	1
La_V478_WL	+ (0.130)V475_WL + V478_WL	9.13e-01	2.30e-02	9.48e-01	3.09e-02	0.983768	0.824	0.788	1
La_V296_NBI	- (13.104)V198_NBI + V296_NBI	-3.21e+02	1.47e+03	3.76e+02	9.94e+02	0.034643	0.810	0.758	-1

1.10 Comparing IDeA vs PCA vs EFA

1.10.1 PCA

featuresnames <- colnames(dataframe)[colnames(dataframe) != outcome]
pc <- prcomp(dataframe[,iscontinous],center = TRUE,scale. = TRUE)   #principal components
predPCA <- predict(pc,dataframe[,iscontinous])
PCAdataframe <- as.data.frame(cbind(predPCA,dataframe[,!iscontinous]))
colnames(PCAdataframe) <- c(colnames(predPCA),colnames(dataframe)[!iscontinous]) 
#plot(PCAdataframe[,colnames(PCAdataframe)!=outcome],col=dataframe[,outcome],cex=0.65,cex.lab=0.5,cex.axis=0.75,cex.sub=0.5,cex.main=0.75)

#pander::pander(pc$rotation)


PCACor <- cor(PCAdataframe[,colnames(PCAdataframe) != outcome])


  gplots::heatmap.2(abs(PCACor),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "PCA Correlation",
                    cexRow = 0.5,
                    cexCol = 0.5,
                     srtCol=45,
                     srtRow= -45,
                    key.title=NA,
                    key.xlab="Pearson Correlation",
                    xlab="Feature", ylab="Feature")

1.10.2 EFA

EFAdataframe <- dataframeScaled

if (length(iscontinous) < 2000)
{
  topred <- min(length(iscontinous),nrow(dataframeScaled),ncol(predPCA)/2)
  if (topred < 2) topred <- 2
  
  uls <- fa(dataframeScaled[,iscontinous],nfactors=topred,rotate="varimax",warnings=FALSE)  # EFA analysis
  predEFA <- predict(uls,dataframeScaled[,iscontinous])
  EFAdataframe <- as.data.frame(cbind(predEFA,dataframeScaled[,!iscontinous]))
  colnames(EFAdataframe) <- c(colnames(predEFA),colnames(dataframeScaled)[!iscontinous]) 


  
  EFACor <- cor(EFAdataframe[,colnames(EFAdataframe) != outcome])
  
  
    gplots::heatmap.2(abs(EFACor),
                      trace = "none",
    #                  scale = "row",
                      mar = c(5,5),
                      col=rev(heat.colors(5)),
                      main = "EFA Correlation",
                      cexRow = 0.5,
                      cexCol = 0.5,
                       srtCol=45,
                       srtRow= -45,
                      key.title=NA,
                      key.xlab="Pearson Correlation",
                      xlab="Feature", ylab="Feature")
}

1.11 Effect on CAR modeling

par(op)
par(xpd = TRUE)
dataframe[,outcome] <- factor(dataframe[,outcome])
rawmodel <- rpart(paste(outcome,"~."),dataframe,control=rpart.control(maxdepth=3))
pr <- predict(rawmodel,dataframe,type = "class")

  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(rawmodel,main="Raw",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(rawmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,dataframe[,outcome]==0))
  }

pander::pander(table(dataframe[,outcome],pr))

	0	1
0	17	4
1	3	52

pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.908	0.819	0.962
3	se	0.945	0.849	0.989
4	sp	0.810	0.581	0.946
6	diag.or	73.667	14.963	362.674

par(op)
par(xpd = TRUE)
DEdataframe[,outcome] <- factor(DEdataframe[,outcome])
IDeAmodel <- rpart(paste(outcome,"~."),DEdataframe,control=rpart.control(maxdepth=3))
pr <- predict(IDeAmodel,DEdataframe,type = "class")

  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(IDeAmodel,main="IDeA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(IDeAmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,DEdataframe[,outcome]==0))
  }

pander::pander(table(DEdataframe[,outcome],pr))

	0	1
0	18	3
1	1	54

pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.947	0.871	0.985
3	se	0.982	0.903	1.000
4	sp	0.857	0.637	0.970
6	diag.or	324.000	31.676	3314.066

par(op)
par(xpd = TRUE)
PCAdataframe[,outcome] <- factor(PCAdataframe[,outcome])
PCAmodel <- rpart(paste(outcome,"~."),PCAdataframe,control=rpart.control(maxdepth=3))
pr <- predict(PCAmodel,PCAdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
  plot(PCAmodel,main="PCA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
  text(PCAmodel, use.n = TRUE,cex=0.75)
  ptab <- epiR::epi.tests(table(pr==0,PCAdataframe[,outcome]==0))
}

pander::pander(table(PCAdataframe[,outcome],pr))

	0	1
0	15	6
1	2	53

pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.895	0.803	0.953
3	se	0.964	0.875	0.996
4	sp	0.714	0.478	0.887
6	diag.or	66.250	12.104	362.601

par(op)

1.11.1 EFA

  EFAdataframe[,outcome] <- factor(EFAdataframe[,outcome])
  EFAmodel <- rpart(paste(outcome,"~."),EFAdataframe,control=rpart.control(maxdepth=3))
  pr <- predict(EFAmodel,EFAdataframe,type = "class")
  
  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(EFAmodel,main="EFA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(EFAmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,EFAdataframe[,outcome]==0))
  }

  pander::pander(table(EFAdataframe[,outcome],pr))

	0	1
0	16	5
1	0	55

  pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.934	0.853	0.978
3	se	1.000	0.935	1.000
4	sp	0.762	0.528	0.918
6	diag.or	Inf	NA	Inf

  par(op)